Childs hauled in a perfect pass from Ryan Mallett on the left sideline and broke a 24-24 tie that Georgia (1-2, O-2 SEC) had forged with two TDs earlier in the quarter.
Mallett was 21-of-33 for 380 yards passing and three touchdowns for the 13th-ranked Razorbacks (3-0, 1-0), who snapped a six-game losing streak against Georgia.
Georgia's Aaron Murray was 15-of-27 for 253 yards and one touchdown. Washaun Ealey ran for 84 yards and scored a touchdown that tied the game with 3:55 to play.
Murray, a redshirt freshman, led two consecutive scoring drives in the fourth quarter after trailing 24-10 after three periods. The drive that tied the game began when the Razorbacks were forced to punt from their own goal line and the ball was downed at the Arkansas 40-yard line.